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An experienced math teacher comes back re: pedagogy
[[User:SamHB|SamHB]] 11:27, 5 December 2008 (EST)
[[User:SamHB|SamHB]] 11:27, 5 December 2008 (EST)
::SamHB, what a surprise. Another "Open Letter to Ed Poor", albeit with a slightly different title. And as usual, it mixes in legitimate concerns with swipes at editors. I agree with you that it's important that the math articles don't get watered down to too low of a level. I'll totally give you that. But, I won't give you the swipe from aside about the Axiom of Choice article. It is not a poor article, in fact it's had numerous contributions to get it to its informative state, including several from Andy himself. We are one of the few places where students can learn about the implications of the Axiom of Choice before being compelled to use it in all their proofs. People who have tried to change that in the past, and we have kept steadfast to our position. If it's a block magnet, it's only because people like you don't agree with the article's position and want to change it to your own. -[[User:Foxtrot|Foxtrot]] 14:29, 5 December 2008 (EST)
::SamHB, what a surprise. Another "Open Letter to Ed Poor", albeit with a slightly different title. And as usual, it mixes in legitimate concerns with swipes at editors. I agree with you that it's important that the math articles don't get watered down to too low of a level. I'll totally give you that. But, I won't give you the swipe from aside about the Axiom of Choice article. It is not a poor article, in fact it's had numerous contributions to get it to its informative state, including several from Andy himself. We are one of the few places where students can learn about the implications of the Axiom of Choice before being compelled to use it in all their proofs. People who have tried to change that in the past, and we have kept steadfast to our position. If it's a block magnet, it's only because people like you don't agree with the article's position and want to change it to your own. -[[User:Foxtrot|Foxtrot]] 14:29, 5 December 2008 (EST)
:::Sam's open letter would be more interesting if I knew who he was. But I disagree with his high/low caution. We don't need a "one size fits all" approach to any topic. Anything that's hard to grasp, like genetics or molecular biology, will need an introductory article. Wikipedia has more than one article whose title is like, "Introduction to X". [http://en.wikipedia.org/w/index.php?title=Special%3AAllPages&from=Introduction+to+Algorithms&to=Introductionz&namespace=0] Some topics can be covered in a single middle-level article. Usually, we have a simply intro - which tells the reader what we're going to tell him; then the we tell him (in the body). But a complex subject may require multiple articles. Wikipedia has '''over 100 articles''' trying to explain evolution. Which by the way shows it's not a simple topic. So we shouldn't dismiss the controversy over it by saying, "Well, the experts say it has been proven." We can prove that Galileo was right (and Aristotle was wrong) with a single, 10-second demonstration. So don't tell me science has to be complicated.
:::Math is complex enough that it requires division into multiple levels. We need at least three, and I wouldn't be dismayed to end up with 4 or 5. Arithmetic starts with counting (and the definition of [[whole numbers]] vs. [[counting numbers]] (see [[Integer]]). Then we get addition and subtraction, which in turn provide the basis for multiplication and division. Next, we teach fractions and decimals. While we're doing this, we try to bring out rules such as the commutative and distributive laws, but kids aren't really tested on this.
:::The next jump is to using variables ("unknowns"). Actually, we start by using blank spaces marked with underscores: 2 = 7 - ________ and then progress to clever shapes like a box! Somewhere between 6th grade and 9th grade we *gasp* take the astonishing step of using a letter like ''x'' for the unknown. It seems kids have to be somewhere around 12 years old to be able to do abstract reasoning like that (see [[Piaget]]). From there we make rapid progress through algebra (or "[[school algebra]]" if you like showing off), plane geometry, trigonometry and what high schools like to call "advanced mathematics" - meaning [[analytic geometry]], [[differential calculus]] and [[integral calculus]].
:::Math majors at college and in grad school get to study on the next couple levels.
:::Now what I am proposing - and I'll probably move this thread to the appropriate page - is that we focus on the first 2 or 3 levels before spending too much time on the upper couple of levels. --[[User:Ed Poor|Ed Poor]] <sup>[[User talk:Ed Poor|Talk]]</sup> 18:32, 6 December 2008 (EST)